"I was in the audience for the taping. Bolton was booed when taking the stage, at which point one of the show's producers hissed at us and said something about "allowing a fair debate". In spite of that, he was then booed overwhelmingly after giving his back-handed insult of an answer to the young vet at the microphone. You can hear a bit of her hissing and shushing again during the clip when the boos start up." - Via r/Libertarian

Note, this isn't the first time FOX was caught editing out boos and replacing it with applause, one year ago FOX was caught editing footage from CPAC where Ron Paul won the straw poll and was cheered, they edited the cheers out and replaced them with boos! They later said it was a "mistake" and they just so happened to have edited in footage from the previous year.

UPDATE: Stossel just released the full unedited video of the question at hand. It shows the vet was edited out of the clip and John Bolton was not cheered, but it does not show he was booed after his response was over.

In the unedited clip you can hear a slight hiss/murmur after Bolton's response at which point the vet responds saying, "Nothing was violated sir, that's what I'm saying.."

Stossel cuts him off and says, "Well, we can't debate this whole thing now, let's just go on to one more questioner, thank you."

At that point there was some applause which seemed to me to be directed towards the vet, whom Stossel just thanked, and not Bolton. (This was all cut, regardless, but Stossel seems to think this was the applause edited into the footage which actually aired, it wasn't.)

Another person in a black shirt then gets to the mic, this is the person seen in the edited video above leaving after the vet's question was asked, he asks a different question on internet freedom which Stossel says they cut due to time, Bolton is applauded after it (he gave a populist response) and Stossel announces the end of the segment and teases the next one. (This is the footage they seamlessly edited in which gave the impression Bolton got applause. It should be noted Fox overlaid applause before Bolton's response was even done, where there should have been silence while he was finishing his statement, there was instead applause. [1:44-1:45])

The two videos frankly give a very different impression, while Stossel says it was an edit due to time, which is believable (and certainly, much more believable than Fox's claim from last year they accidentally edited in footage from the previous year's CPAC), the editing still gave a very different impression from what actually happened.